binomni koeficijent
Definicija: broj oblika \(\frac{n!}{k! (n-k)!}\) za određene prirodne brojeve \(n\) i \(k\), \(n \geq k\) pri čemu \(k\) može biti i nula
Školska definicija: Binomni koeficijent je broj oblika \(\frac{(n-0)\cdot(n-1)\cdot(n-2)\cdots (n-(k-1))}{k\cdot (k-1)\cdot (k-2) \cdots 1}\). Binomni koeficijent može se prikazati i pomoću faktorijela \(\frac{n!}{k! (n-k)!}\)
Napomena: Binomni koeficijenti koeficijenti su polinoma dviju varijabli koji se pojavljuju u binomnom poučku \((x+y)^n = \sum_{k=0}^n \frac{n!}{k! (n-k)!} x^k y^{n-k}\).
Simbol: \(\binom{n}{k}\)
Engleske istovrijednice: binomial coefficient
Njemačke istovrijednice: Binomialkoeffizient
Struna ID: 32765
Obrađivač: Zoran Škoda
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WMW naziv: binomial coefficient
WMW klasifikacija: Discrete Mathematics > Combinatorics > Binomial Coefficients >
WMW definicija: The binomial coefficient \(\binom{n}{k}\) is the number of ways of picking \(k\) unordered outcomes from \(n\) possibilities, also known as a combination or combinatorial number.
WMW napomena: The symbols \({}_nC_k\) and \(\binom{n}{k}\) are used to denote a binomial coefficient, and are sometimes read as "\(n\) choose \(k\)".
WMW See also: Apéry Number, Balanced Binomial Coefficient, Ballot Problem, Bernoulli Triangle, Binomial, Binomial Distribution, Binomial Identity, Binomial Sums, Binomial Theorem, Central Binomial Coefficient, Choose, Christmas Stocking Theorem, Chu-Vandermonde Identity, Combination, Deficiency, Erdős Squarefree Conjecture, Exceptional Binomial Coefficient, Factorial, Fibonomial Coefficient, Gamma Function, Good Binomial Coefficient, k-Subset, Kings Problem, Klee's Identity, Lah Number, Multichoose, Multinomial Coefficient, Pascal's Formula, Permutation, q-Binomial Coefficient, Roman Coefficient, Sárkőzy's Theorem, Stanley's Identity, Star of David Theorem, Stolarsky-Harborth Constant, Strehl Identities, Székely Identity, Wolstenholme's Theorem
Izvor: Weisstein, Eric W. "Binomial Coefficient." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/BinomialCoefficient.html
Struna ID: 32765